Answer:
The solution is 
Step-by-step explanation:
The equation
can be rewritten as
and can be further simplified to
.
Now, taking the inverse sine of both sides we get:
The value of the right side on the interval 
is
,
which makes the equation (2)
solving for 
gives
which is our solution.
Thanks for posting your question here. The answer to the above problem is x = <span>48.125. Below is the solution:
</span>
x+x/7+1/11(x+x/7)=60
x = x/1 = x • 7/7
x <span>• 7 + x/ 7 = 8x/7 - 60 = 0
</span>x + x/7 + 1/11 <span>• 8x/7 - 60 = 0
</span>8x <span>• 11 + 8x/ 77 = 96x/ 77
</span>96x - 4620 = 12 <span>• (8x-385)
</span>8x - 385 = 0
x = 48.125
Let x = speed of the first car
the second car is 12 km slower so the seconds car speed is x-12
they each drove 2 hours so 1st car = 2x
2nd car = 2(x-12)
they drove 360 km
so you have 2x + 2(x-12) = 360
solve for x
2x+2(x-12) = 360
2x + 2x-24 = 360
4x-24 = 360
4x = 384
x = 384/4
x = 96
1st car drove at 96 km per hour
slower car drove at 96-12 = 84 km per hour
There are several approaches.
(5/3)x^2 - 5 = 0 has the coefficients a=5/3, b=0 and c = -5.
Thus, the quadratic formula would be appropriate here:
-0 plus or minus sqrt(0^2 - 4(5/3)(-5) )
x = -------------------------------------------------------
2(5/3)
plus or minus sqrt(100/3)
= ------------------------------------
10/3
3 10
= ------* ----------- = sqrt(3) (answer)
10 sqrt(3)
